use the graph to determine\na. open intervals on which the function is increasing, if any.\nb. open…
use the graph to determine\na. open intervals on which the function is increasing, if any.\nb. open intervals on which the function is decreasing, if any.\nc. open intervals on which the function is constant, if any.\na. select the correct choice below and, if necessary, fill in the answer box to complete your choice\noa. the function is increasing on the interval(s)\n(row your answer in interval notation. use a comma to separate answers as needed)\nob. there is no interval on which the function is increasing
Answer
Explanation:
Step1: Recall the definition of an increasing function
A function (y = f(x)) is increasing on an open interval ((a,b)) if for any (x_1,x_2\in(a,b)) with (x_1 < x_2), we have (f(x_1)<f(x_2)). Visually, the graph of the function rises from left - to - right on an increasing interval.
Step2: Analyze the given graph
Looking at the graph, we can see that the function rises (is increasing) on two intervals.
- The first increasing interval: We start from the left - hand side of the graph. The function starts to rise from (x=-3) (not included) to (x = - 1) (not included). In interval notation, this is ((-3,-1)).
- The second increasing interval: The function also rises from (x = 1) (not included) to the right - hand side of the graph. In interval notation, this is ((1,\infty)).
Answer:
A. The function is increasing on the intervals ((-3,-1)) and ((1,\infty))